This game looks incredible, and I love the core idea.
On some very high level of abstraction this is almost the same balance of decisions as racing: you can choose to go faster/use more power, but it's gonna be more dangerous. But in case of racing you can build up skill to learn to control the power so you can go fast *and* be precise while doing it, and that's what lets you win. I guess that is the feeling I was missing here: some more control so you can feel that your victories aren't pure luck and your losses aren't just unfair.
Maybe after setting the power there could be some simple minigame-type interaction that would determine how successful the next shot is going to be. It would be a metaphor for aiming with an unstable weapon. For example:
Power 1: You just pick a square and shoot, done. Power 2-4: You pick a square and see highlighted area of possible hits. A UI appears for precise aiming: a bar with a narrow green zone and a mark going quickly left and right, and you have to stop it in the green zone — kind of like a "default fishing mini-game" to determine the success of your shot based on how close you get. The closer you get, the more enemies in the zone will get hit (min = 0, max = power level). At power 2 it's easy and you win almost every time, but at power 4 it's so quick that you almost rely completely on luck, but not quite, because whatever the outcome of the minigame, it's still on you!
That's just one idea of how to achieve the feeling I was missing, no doubt there could be numerous other solutions. And, well, it's just an idea, not saying the current completely random shooting is necessarily worse. Just thinking aloud :)
Also, would be nice to maybe have an option to play with the keyboard: WASD + Q/E for setting power + Space to shoot would feel pretty nice imo. Mouse interactions make it a bit slow for my taste.
Sorry for the huge comment, this just shows you how much I liked what you made :) Your entry is awesome.